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    I need to Show that X^4+5x^3+6x^2-4x-8= (x^2+x-2)(x^2+4x+4)

    but I am not too sure how to go about doing this- I was thinking of doing long division and then obtaining a polynomial with 3rd degree?
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    (Original post by FloralEssence)
    I need to Show that X^4+5x^3+6x^2-4x-8= (x^2+x-2)(x^2+4x+4)

    but I am not too sure how to go about doing this- I was thinking of doing long division and then obtaining a polynomial with 3rd degree?
    If the question does say "show" then all you need to do is expand the right-hand-side and show it equals the left.

    It would be good if you post a picture of the question or post the question exactly as you see it (if you haven't already).
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    (Original post by FloralEssence)
    I need to Show that X^4+5x^3+6x^2-4x-8= (x^2+x-2)(x^2+4x+4) but I am not too sure how to go about doing this- I was thinking of doing long division and then obtaining a polynomial with 3rd degree?
    You could expand RHS. Or Look at the RHS find suitable factor e.g. (x-1) and use the factor theorem to show when x=1 f(x) is 0 then do algebraic division and repeating substituting in suitable values
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    (Original post by notnek)
    If the question does say "show" then all you need to do is expand the right-hand-side and show it equals the left.

    It would be good if you post a picture of the question or post the question exactly as you see it (if you haven't already).
    Hey!
    This is the question, and I am asked to prove from left to right, i.e. do the factorisation of some sort such that I may obtain the RHS


    Show x^4 + 5x^3 + 6x^2 −4x−8 = (x^2 + x−2)(x^2 + 4x + 4). Hence sketch the curve y = f(x)where f(x) = x4 +5x3 +6x2−4x−8, showing all points of interest.
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    (Original post by FloralEssence)
    Hey!
    This is the question, and I am asked to prove from left to right, i.e. do the factorisation of some sort such that I may obtain the RHS


    Show x^4 + 5x^3 + 6x^2 −4x−8 = (x^2 + x−2)(x^2 + 4x + 4). Hence sketch the curve y = f(x)where f(x) = x4 +5x3 +6x2−4x−8, showing all points of interest.
    As I said before, since you're given the factorisation and are asked to "show", you just need to expand the brackets and show that this is equal to the polynomial.
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    so everyone else has already answered ur question BUT,
    if the exams come and ur stuffed while trying to answer one just go with the good ol' factor theorem. Find what x values give f(x)=0, -ve value is the factor, find as many simple ones as you can and you either multiply some brackets or re-arrange a couple. (4 brackets has more than 1 configuration therefore multiple [equivalent] quadratic factors)
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    (Original post by Xenon17)
    You could expand RHS. Or Look at the RHS find suitable factor e.g. (x-1) and use the factor theorem to show when x=1 f(x) is 0 then do algebraic division and repeating substituting in suitable values
    Yeah, this was what I have been trying to do

    I managed to get x^3+6x^2+12x+8

    then, I continued- I found that x-2 was a factor of the above result.

    I did long division and obtained x^2+4x+4

    -----------------------------------

    EDIT:

    Oh, guys, I found the result! sorry- I multiplied the factors (x-1)(x-2) out and got x^2+x-2

    then pairing up with x^2+4x+4

    would give me the answer.

    Thanks to the contributers!
 
 
 
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